A fundamental goal of compression is to reduce the amount of data necessary to represent the original object, while maintaining fidelity and important features. Examples of important applications include: data transmission, data storage and data retrieval.
Many existing methods are of limited use because they cannot achieve a high compression ratio with good image fidelity, or because they do not have tractable computational complexity. For many methods high compression ratios may introduce unacceptable artifacts such as: ringing, blurring or blocking. Compression of curves or surfaces using standard methods such as NURBS (for “non-uniform rational B-splines”; see, e.g., Rogers, D. F., An Introduction to NURBS: with Historical Perspective, Morgan-Kaufmann (2000), which is incorporated herein by reference) becomes difficult if the curves or surfaces are deformed (even slightly) so as to change topology. This may occur, for instance, if the viewing resolution is changed. Moreover, standard curve or surface compression methods do not allow for computational ease in computing geometric properties of the curve or surface, e.g., normals and curvatures.
Standard quantization techniques do not take into account geometrical properties of the features, e.g., edges, textures. For example, a widely used standard quantization method divides the intensity range into equal integer values and blindly converts the intensity values to the nearest integers. Another popular method equalizes the area histogram. These methods often lead to loss of important features.